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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2004 Switzerland Team Selection Test
7
7
Part of
2004 Switzerland Team Selection Test
Problems
(1)
a =\sqrt{45-\sqrt{21-a}}, b =\sqrt{45+\sqrt{21-b}}, c =\sqrt{45-\sqrt{21+c}},
Source: Switzerland - Swiss TST 2004 p7
2/18/2020
The real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
satisfy the equations:
{
a
=
45
−
21
−
a
b
=
45
+
21
−
b
c
=
45
−
21
+
c
d
=
45
+
21
+
d
\begin{cases} a =\sqrt{45-\sqrt{21-a}} \\ b =\sqrt{45+\sqrt{21-b}}\\ c =\sqrt{45-\sqrt{21+c}}\ \\ d=\sqrt{45+\sqrt{21+d}} \end {cases}
⎩
⎨
⎧
a
=
45
−
21
−
a
b
=
45
+
21
−
b
c
=
45
−
21
+
c
d
=
45
+
21
+
d
Prove that
a
b
c
d
=
2004
abcd = 2004
ab
c
d
=
2004
.
system of equations
Product
algebra